There are \( 5 \) students in class \( 10 \), \( 6 \) students in class \( 11 \) and \( 8 \) students in class \( 12 \). If the number of ways, in which \( 10 \) students can be selected from them so as to include at least \( 2 \) students from each class and at most \( 5 \) students from the total \( 11 \) students of class \( 10 \) and \( 11 \) is \( 100k \), then \( k \) is equal to ____________ .
